library(simmer)
library(simmer.plot)Ejemplo modelo de puntos referenciados
Examples with simmer
Simpler example: one server and many clients arriving at random
Consider a single server with service time N(10,4) and clients have interarrival times exp(1/5) (one client every five minutes)
client <-
trajectory("Client") %>%
#log_("Here I am") %>% # can send a message for each arrive
seize("server") %>%
timeout(function() rnorm(1,10,2)) %>% # service time
release("server") # %>%
#log_("Finished")
shop <-
simmer("shop") %>% #initializes a simulation environment
add_resource("server", 1) %>%
add_generator("Client", client, function() rexp(1,1/5))
# Run a replication 100 minutes.
shop %>% run(until = 100)simmer environment: shop | now: 100 | next: 101.673684204213
{ Monitor: in memory }
{ Resource: server | monitored: TRUE | server status: 1(1) | queue status: 10(Inf) }
{ Source: Client | monitored: 1 | n_generated: 20 }# Monitor arrivals of clients, and compute the waiting time in queue
# activity_time is service time.
shop %>%
get_mon_arrivals() %>%
transform(waiting_time = end_time -start_time - activity_time) name start_time end_time activity_time finished replication waiting_time
1 Client0 2.463082 12.68849 10.225405 TRUE 1 -1.776357e-15
2 Client1 12.964034 22.12465 9.160620 TRUE 1 1.776357e-15
3 Client2 18.093027 34.38824 12.263582 TRUE 1 4.031627e+00
4 Client3 25.837158 41.90508 7.516842 TRUE 1 8.551077e+00
5 Client4 31.499937 54.04382 12.138744 TRUE 1 1.040514e+01
6 Client5 38.826483 66.59546 12.551642 TRUE 1 1.521734e+01
7 Client6 41.492093 81.92253 15.327064 TRUE 1 2.510337e+01
8 Client7 46.588726 93.26013 11.337601 TRUE 1 3.533380e+01# Monitor server
shop %>% get_mon_resources() resource time server queue capacity queue_size system limit replication
1 server 2.463082 1 0 1 Inf 1 Inf 1
2 server 12.688487 0 0 1 Inf 0 Inf 1
3 server 12.964034 1 0 1 Inf 1 Inf 1
4 server 18.093027 1 1 1 Inf 2 Inf 1
5 server 22.124654 1 0 1 Inf 1 Inf 1
6 server 25.837158 1 1 1 Inf 2 Inf 1
7 server 31.499937 1 2 1 Inf 3 Inf 1
8 server 34.388236 1 1 1 Inf 2 Inf 1
9 server 38.826483 1 2 1 Inf 3 Inf 1
10 server 41.492093 1 3 1 Inf 4 Inf 1
11 server 41.905077 1 2 1 Inf 3 Inf 1
12 server 46.588726 1 3 1 Inf 4 Inf 1
13 server 49.898850 1 4 1 Inf 5 Inf 1
14 server 50.328328 1 5 1 Inf 6 Inf 1
15 server 54.043821 1 4 1 Inf 5 Inf 1
16 server 56.358919 1 5 1 Inf 6 Inf 1
17 server 66.595463 1 4 1 Inf 5 Inf 1
18 server 66.864360 1 5 1 Inf 6 Inf 1
19 server 70.328969 1 6 1 Inf 7 Inf 1
20 server 71.395474 1 7 1 Inf 8 Inf 1
21 server 81.922527 1 6 1 Inf 7 Inf 1
22 server 86.772002 1 7 1 Inf 8 Inf 1
23 server 88.489641 1 8 1 Inf 9 Inf 1
24 server 89.081534 1 9 1 Inf 10 Inf 1
25 server 93.107387 1 10 1 Inf 11 Inf 1
26 server 93.260128 1 9 1 Inf 10 Inf 1
27 server 95.516017 1 10 1 Inf 11 Inf 1# Monitoring the process
resources <- get_mon_resources(shop)
plot(resources, metric = "utilization")
plot(resources, metric = "usage", steps = T)
Replications of the simulations
Simulate the process for 8 hrs (8*60 = 480 minutes) and replicate 100 times
# simulate 8 hours 100 times
envs <- lapply(1:100,
function(i) {
simmer("shop") %>%
add_resource("server",1) %>%
add_generator("Client", client, function() rexp(1, 1/5)) %>%
run(until = 480)})We can obtain performance metrics from the runs
plot(get_mon_resources(envs), metric = "utilization")
plot(get_mon_resources(envs), metric = "usage", items = "server")
plot(get_mon_arrivals(envs), metric = "waiting_time")`geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'
Consider adding a total of three servers
# simulate 8 hours 100 times
envs <- lapply(1:100,
function(i) {
simmer("shop") %>%
add_resource("server",3) %>%
add_generator("Client", client, function() rexp(1, 1/5)) %>%
run(until = 480)})plot(get_mon_resources(envs), metric = "utilization")
# number of servers busy during the day
plot(get_mon_resources(envs), metric = "usage", items = "server")
# number of clients waiting for service
plot(get_mon_resources(envs), metric = "usage", items = "queue")
# waiting time
plot(get_mon_arrivals(envs), metric = "waiting_time")`geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'
Several counters with individual queues
Each counter is assumed to have its own queue. Each client has to decide which queue to join, usually decides to join the shortest queue. There are several policies that can be considered
shortest-queue: the resource selects the shortest queueround-robin: resources will be selected in a cyclical naturefirst-available: the first available resource is selectedrandom: a resource is randomly selected
client <-
trajectory("Client") %>%
select(c("server1", "server2"), policy = "shortest-queue") %>%
seize_selected() %>%
timeout(function() rnorm(1,10,4)) %>%
release_selected()
shop <-
simmer("shop") %>%
add_resource("server1", 1) %>%
add_resource("server2", 1) %>%
add_generator("Client", client, function() rexp(1, 1/5))
run(shop, until = 240)simmer environment: shop | now: 240 | next: 249.35399741207
{ Monitor: in memory }
{ Resource: server1 | monitored: TRUE | server status: 1(1) | queue status: 0(Inf) }
{ Resource: server2 | monitored: TRUE | server status: 1(1) | queue status: 0(Inf) }
{ Source: Client | monitored: 1 | n_generated: 45 }# Monitoring the process
resources <- get_mon_resources(shop)
plot(resources, metric = "utilization")
plot(resources, metric = "usage", steps = T)
Simulate a ambulatory consultation service
First a patient is seen by a nurse for preliminary steps. Then the patient is seen by two doctors for the consultation and finally by administrative staff to schedule a follow-up appointment or other tasks.
Construct a patient trajectory defining the previous steps
patient <- trajectory("patients") %>%
## add nurse
seize("nurse",1) %>%
timeout(function() rnorm(1, 15)) %>%
release("nurse", 1) %>%
## add a consultation activity
seize("doctor", 2) %>%
timeout(function() rnorm(1, 20)) %>%
release("doctor", 2) %>%
## add a planning activity
seize("admin", 1) %>%
timeout(function() rnorm(1, 5)) %>%
release("admin", 1)
plot(patient) Now attach arrivals and define the resources needed with capacities
envs <- lapply(1:100, function(i) {
simmer("health center") %>%
add_resource("nurse", 3) %>%
add_resource("doctor", 4) %>%
add_resource("admin", 2) %>%
add_generator("patient", patient, function() rexp(1, 1/5)) %>%
run(until=480)})plot(get_mon_resources(envs), metric = "utilization")
plot(get_mon_resources(envs), metric = "usage", items = "server")
plot(get_mon_arrivals(envs), metric = "waiting_time")`geom_smooth()` using method = 'gam' and formula = 'y ~ s(x, bs = "cs")'